Environmental Engineering Reference
In-Depth Information
in which
W
is the average shear stress of the flow at the channel bed and banks;
p
B
and
p
w
are the wet
perimeter at the bed and banks, respectively; and u is the velocity of the flowing column.
The released potential energy of solid materials is
' ' ' (11.42)
in which U is the density of sediment; ' is the depth of the channel bed incision;
d
L
and
L
L
are the
thickness and length of the sliding layer from the left bank, respectively;
d
R
and
L
R
are the thickness and
length of the sliding layer from the right bank, respectively; and
Q
S
is the sediment discharge at position 2.
According to Bagnold (1988), collisions between the solid particles create a dispersive stress on the
channel bed
T:
e
U
gS Bh
(
d L
d L
)
x
U
gSQt
2
s
L
L
R
R
s
s
2
w
u
§
·
p
2
T
0.013
UO
(
D
)
¹
(11.43)
¨
¸
s
w
z
©
in which
D
is the diameter of particles;
u
p
is the velocity of particles; O is the linear concentration
defined by Bagnold (1954):
1
O
(11.44)
1/3
§
·
C
C
v
*
1
¨
¸
©
¹
v
where C
v*
is the maximum concentration for sediment when the particles compactly piled, which is equal
to 0.73 for uniform round particles (Bagnold, 1954).
The energy consumption due to collision of solid particles is given by
4
e Bx ut
' '
(11.45)
Substituting Eqs. (11.40-11.42) and Eq. (11.45) into Eq. (11.39) yields
'
E
w
E
k
k
U
gSQ
W
0
(
p
p
)
u
U
gSQ
TBu
|
(11.46)
B
w
s
s
'
t
w
t
In general, the released potential energy of water balances the friction at the wet perimeter. If the third
term in the equation, or the released energy from the solid materials, is large or equal to the fourth term,
or the energy consumption due to collision of solid particles, the kinetic energy increases or remain
constant. The flow may continuously scour the channel bed and banks and more and more sediment
enters the flow, and finally, the flow develops into a debris flow. If the gradient of the gully is high the
third term is larger than the fourth term. Development of debris flow depends on the incision of the bed
and collapse of banks. In this case the bed structure of step-pools becomes the key for debris flow control.
If there are no bed structures or bed structures are destroyed, the gully bed can be scoured by torrential
flood, which in turn causes bank collapses. The sediment entering into the flow does not cause reduction
of the kinetic energy of the flow. Thus, a disastrous flow of water and high concentration of solid
materials occurs. The debris flows occurring in Wenjiagou in 2010 illustrated the theory. If the solid
materials consist of a lot of large stones, the fourth term in the equation may slightly larger than the third
term because
T
is proportional to the square of the diameter
D
2
. The kinetic energy may reduce until the
velocity becomes small.
Figure 11.69 shows the longitudinal bed profile of the new Wenjiagou Gully after the debris flow in
2010. The bed profiles in 2008 and 2009 are shown as a comparison, on which locations of the 20 dams
are indicated. For the gully reach of 1,300 m-1,800 m from the gully mouth the landslide buried the gully
with a thickness of about 150 m. In 2008 debris flows scoured the landslide deposit by about 50 m and
formed the new Wenjiagou channel. In 2009 the step-pool system controlled debris flows and stabilized
the channel bed. The bed profile remained the same as in 2008. In 2010 the new channel bed was again
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